How do you write the first five terms of the sequence a_n=10/n^(2/3)?

Jun 6, 2017

$10 , \frac{10}{\sqrt[3]{4}} , \frac{10}{\sqrt[3]{9}} , \frac{10}{\sqrt[3]{16}} , \frac{10}{\sqrt[3]{25}}$

Explanation:

We have: ${a}_{n} = \frac{10}{{n}^{\frac{2}{3}}}$

To evaluate the first five terms, simply replace $n$ with the number of the term:

$R i g h t a r r o w {a}_{1} = \frac{10}{{1}^{\frac{2}{3}}} = \frac{10}{1} = 10$

$R i g h t a r r o w {a}_{2} = \frac{10}{{2}^{\frac{2}{3}}} = \frac{10}{{\left({2}^{2}\right)}^{\frac{1}{3}}} = \frac{10}{\sqrt[3]{4}}$

$R i g h t a r r o w {a}_{3} = \frac{10}{{3}^{\frac{2}{3}}} = \frac{10}{{\left({3}^{2}\right)}^{\frac{1}{3}}} = \frac{10}{\sqrt[3]{9}}$

$R i g h t a r r o w {a}_{4} = \frac{10}{{4}^{\frac{2}{3}}} = \frac{10}{{\left({4}^{2}\right)}^{\frac{1}{3}}} = \frac{10}{\sqrt[3]{16}}$

$R i g h t a r r o w {a}_{5} = \frac{10}{{5}^{\frac{2}{3}}} = \frac{10}{{\left({5}^{2}\right)}^{\frac{1}{3}}} = \frac{10}{\sqrt[3]{25}}$

Therefore, the first five terms of the sequence are $10 , \frac{10}{\sqrt[3]{4}} , \frac{10}{\sqrt[3]{9}} , \frac{10}{\sqrt[3]{16}}$ and $\frac{10}{\sqrt[3]{25}}$